![]() “Reduction in any way can eventually produce the same result.” ![]() If E1 ↔ E2, then there exists an E such that E1 → E and E2 → E. The Church-Rosser Theorem states the following − For Example − Alpha ReductionĪlpha reduction is very simple and it can be done without changing the meaning of a lambda expression. ![]() E) y replaces every x that occurs free in E with y. In an expression, each appearance of a variable is either "free" (to λ) or "bound" (to a λ). The inner x belongs to the inner λ and the outer x belongs to the outer one. When there are multiple terms, we can handle them as follows − The formal parameter may be used several times − There are two reducible expressions: (* 5 6) and (* 8 3). Here, we can’t start with '+' because it only operates on numbers. Let us evaluate the following expression − Pure lambda calculus has no built-in functions. Where λx.E is called Lambda abstraction and E is known as λ-expressions. Lamdba calculus includes three different types of expressions, i.e., And all the functions are on single argument. These functions can be of without names and single arguments.įunction application − Church used the notation E 1.E 2 to denote the application of function E 1 to actual argument E 2. Lambda calculus is a framework developed by Alonzo Church in 1930s to study computations with functions.įunction creation − Church introduced the notation λx.E to denote a function in which ‘x’ is a formal argument and ‘E’ is the functional body.
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